Question

find: tan a
triangle diagram: right angle, vertical side 48 (labeled b), horizontal side 55 (labeled a), hypotenuse 73
the figure is not drawn to scale
answer
options: (\frac{48}{73}), (\frac{55}{73}), (\frac{55}{48}), (\frac{48}{55})

Explanation:

Step1: Recall tangent definition

In a right triangle, $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$ to $\theta$.

Step2: Identify sides for $\angle A$

For $\angle A$, opposite side is $48$, adjacent side is $55$.

Step3: Calculate $\tan A$

$\tan A = \frac{\text{opposite to } A}{\text{adjacent to } A} = \frac{48}{55}$

Answer:

$\frac{48}{55}$ (corresponding to the option with $\frac{48}{55}$)